On the necessity of the Lindeberg condition for the normal convergence of martingales (Q1566447)
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scientific article; zbMATH DE number 1927747
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the necessity of the Lindeberg condition for the normal convergence of martingales |
scientific article; zbMATH DE number 1927747 |
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On the necessity of the Lindeberg condition for the normal convergence of martingales (English)
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15 June 2003
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The author considers the central limit theorem for a sequence of square-integrable martingales \(S_{n,k},\) \(0\leq k\leq k_n,\) \(S_{n,0}=0\). It is proved that the ``conditional'' Lindeberg condition follows from the normal convergence of sums \(S_{n,k}\) under some conditions. The result is related to the one obtained by \textit{A. G. Sholomitskij} [Theory Probab. Appl. 43, 434-448 (1998); translation from Teor. Veroyatn. Primen. 43, 490-508 (1998; Zbl 0954.60016)]. The conditions in both results are different.
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normal convergence of martingales
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Lindeberg condition
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Lindeberg-Feller theorem
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